Permutations And Combinations Question 111
Question: $ ( \begin{matrix} n \\ n-r \\ \end{matrix} )+( \begin{matrix} n \\ r+1 \\ \end{matrix} ) $ , whenever $ 0\le r\le n-1 $ is equal to [AMU 2000]
Options:
A) $ ( \begin{matrix} n \\ r-1 \\ \end{matrix} ) $
B) $ ( \begin{matrix} n \\ r \\ \end{matrix} ) $
C) $ ( \begin{matrix} n \\ r+1 \\ \end{matrix} ) $
D) $ ( \begin{matrix} n+1 \\ r+1 \\ \end{matrix} ) $
Correct Answer: D $ \Rightarrow {{}^{n}}C _{r}+{{}^{n}}{C _{r+1}} $ = $ ^{n+1}{C _{r+1}}=( \begin{matrix} n+1 \\ r+1 \\ \end{matrix} ) $ .
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Answer:
Solution:
BETA
